Question

I am not sure how to do this problem, if someone can assist.?

The population of viruses in an influenza culture after t hours is given by the function
x(t) = 5e^t/9.1
The cost y in dollars for a new automated microscope to count x viruses in a sample is
y(x) = ln 7x
Create the composite function that calculates the cost y in dollars of counting the number of
viruses in an influential culture after t hours.

Answer 1

`y(t)=t+1.347`
We are obtaining a linear equation in t

Explanation:

Here,

At any time t, population of viruses is
`x(t)=(5e^t)/9.1`

cost y in dollars to count x viruses in a sample is
`y(x)=ln7x`

Substituting for x(t)

`y(t)=ln(7)((5e^t)/9.1)`
By product rule and quotient rule
`y(t)=ln7+ln(5e^t)-ln9.1`
By index rule
`y(t)=ln7+ln5+lne^t-ln9.1`
by basic rule
`y(t)=ln7+ln5+t-ln9.1`
`y(t)=t+ln7+ln5-ln9.1`
`y(t)=t+ln(((7)(5))/(9.1))`
After simplification
`y(t)=t+1.347`
We are obtaining a linear equation in t